Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization
Fabian Hoppe, Ira Neitzel · ESAIM Control Optimisation and Calculus of Variations · 2022
We prove first- and second-order optimality conditions for sparse, purely time-dependent optimal control problems governed by a quasilinear parabolic PDE. In particular, we analyze sparsity patterns of the optimal controls induced by different sparsity enforcing functionals in the purely timedependent control case and illustrate them by numerical examples. Our findings are based on results obtained by abstraction of well known techniques from the literature.